Einleitung zur FEM und erste Formulierungen zur statischen Analyse hinzugefügt

Preamble/Main.tex

@@ -163,6 +163,11 @@
 % -----------------------------------------
 %  Aufzählungen
 % -----------------------------------------
+\makeatletter
+\newcommand*{\rom}[1]{\mathrm{\romannumeral #1}}
+\newcommand*{\Rom}[1]{\mathrm{\expandafter\@slowromancap\romannumeral #1@}}
+\makeatother
+
 \renewcommand{\labelitemi}{--}
 \renewcommand{\labelitemii}{\(\boldsymbol\cdot\)}    % \times
 
@@ -172,8 +177,11 @@
 \setlist{nosep} % noitemsep
 \setlist[1]{labelindent=\parindent} % Usually a good idea
 \setlist[itemize]{parsep=0pt,itemsep=0pt,leftmargin=*}
+\setlist[enumerate]{parsep=0pt,itemsep=0pt,leftmargin=*}
 
 \usepackage{listings}
+%\usepackage{listingsutf8}
+%\begin{lstlisting}[numbersep=0pt,resetmargins=true]
 \renewcommand{\lstlistingname}{Programmausdruck}
 \lstdefinestyle{custom}{
   %xleftmargin=2em,
@@ -186,7 +194,18 @@
   columns=fullflexible,
   basicstyle=\ttfamily % otherwise copy-and-paste won’t work
 }
+\lstset{literate=%
+{Ö}{{\"O}}1
+{Ä}{{\"A}}1
+{Ü}{{\"U}}1
+{ß}{{\ss}}1
+{ü}{{\"u}}1
+{ä}{{\"a}}1
+{ö}{{\"o}}1
+}
 \lstset{
+    extendedchars=\true,
+    %inputencoding=utf8/latin1,  % if package listingsutf8 is used
     style=custom,
     language=Matlab,
     basicstyle=\scriptsize\ttfamily,   % small, footnotesize, scriptsize
@@ -252,6 +271,24 @@
 % linie unterhalb mit text \underbracket[1pt][0pt]{bla}_\text{blo}
 
 \newcommand\Dfrac[2]{\dfrac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\slfrac}[2]{\left.#1\middle/#2\right.}
+\usepackage{xfrac}
+\usepackage{nicefrac}
+\usepackage{faktor}
+% http://tex.stackexchange.com/questions/27591/extending-the-faktor-package/27735#27735
+\DeclareDocumentCommand{\Faktor}{s m O{0.5} m O{-0.5}}{% \newfaktor[*]{#2}[#3]{#4}[#5] -> #2/#4
+  \setbox0=\hbox{\scalebox{0.8}{\ensuremath{#2\vphantom{1}}}}% Store numerator
+  \setbox1=\hbox{\ensuremath{\diagup}}% Store slash /
+  \setbox2=\hbox{\scalebox{0.8}{\ensuremath{#4}}}% Store denominator
+  \raisebox{#3\ht1}{\usebox0}% Numerator
+  \mkern-5mu\ifthenelse{\equal{#1}{\BooleanTrue}}% Slash /
+    {\diagup}% regular \faktor slash
+    {\rotatebox{-44}{\rule[#5\ht2]{0.4pt}{-#5\ht2+#3\ht0+\ht0}}}% tilted rule as a slash
+  \mkern-4mu%
+  \raisebox{#5\ht2}{\usebox2}% Denominator
+}
+
+% another slanted fration below at tikz
 
 
 \usepackage[            % kann nicht mit amssymb zusammenlaufen
@@ -291,16 +328,31 @@
 \newcommand{\LM}{\field{L}}         % Lösungsmenge
 \newcommand*{\qed}{\hfill\ensuremath{\blacksquare}}
 \newcommand*\euler{\mathrm{e}}
+\renewcommand{\deg}{\ensuremath{^{\circ}}\xspace}
+\newcommand\degC{{\,^{\circ}\mathrm{C}}}
+\newcommand\sins{{\mathrm{s}}}      % short sin: s
+\newcommand\coss{{\mathrm{c}}}      % short cos: c
 
-\newcommand{\dif}{\mathrm{d}}
-
+\newcommand{\T}{{\mathrm{T}}\!}     % Transpose operator
+\newcommand{\TF}{{\raisebox{-0.5ex}{$\sim$}}} % sign for transfomed values: low tilde
+\newcommand{\adj}{{\mathrm{H}}}     % Adjoint operator
+\newcommand*\dif{\mathop{}\!\mathrm{d}}
 \newcommand*\E{\ensuremath{\mathrm{E}}}
 
 \providecommand{\norm}[1]{\lVert #1 \rVert}             % ||x||
 \providecommand{\abs}[1]{\lvert #1 \rvert}              % |x|
 \providecommand{\innerProd}[2]{\langle #1, #2\rangle}   % <x,y>
 
-\DeclareMathOperator{\grad}{grad}   % $\grad u$ = grad u
+\DeclareMathOperator{\Bild}{Bild}      % Bild einer Funktion 
+\DeclareMathOperator{\rank}{rank}      % Rank of a matrix 
+\DeclareMathOperator{\tr}{tr}          % Matrix trace
+\DeclareMathOperator{\dev}{dev}        % Matrix deviation
+\DeclareMathOperator{\var}{var}        % Variance 
+\DeclareMathOperator{\grad}{grad}      % $\grad u$ = grad u
+\DeclareMathOperator{\divergence}{div} % $\div u$ = div u
+\DeclareMathOperator{\rot}{rot}        % $\rot u$ = rot u
+\DeclareMathOperator{\diag}{diag}      % Diagonal matrix
+\DeclareMathOperator{\adjugate}{adj}   % Classical adjoint (adjugate) 
 
 %\newcommand{\corresponds}{\ensuremath{\stackrel{\wedge}{=} \hat{=} \mathop{\hat{=}} \substack{\wedge\\=} \mathrel{\widehat{=}} } \^{=} }
 \newcommand*\corresponds{%
@@ -316,13 +368,21 @@
   \overset{\mbox{\large\bfseries .\hspace{-0.1ex}.}}{#1}}
 
 %\usepackage{accents}
+\usepackage{ushort}  % for tensor
+%\usepackage{ulem}    % not for math mode, too much space below with uuline; for tensor
 
+\newcommand{\tensor}[1]{    \ensuremath{ {\boldsymbol{#1}} } }
 
-\newcommand{\tensor}[1]{   \ensuremath{ \mathbf{#1} } }
-\newcommand{\tensorI}[1]{   \ensuremath{ \uline{  \bm{#1} } } }
-\newcommand{\tensorII}[1]{  \ensuremath{ \uuline{ \bm{#1} } } }
-\newcommand{\tensorIII}[1]{ \ensuremath{ \underaccent{3}{ \underaccent{\tilde}{ \bm{#1} } } } }
-\newcommand{\tensorIV}[1]{  \ensuremath{ \underaccent{4}{ \underaccent{\tilde}{ \bm{#1} } } } }
+\newcommand{\tensorI}[1]{   \ensuremath{ \ushort{ {\boldsymbol{#1}} } } }
+\newcommand{\tensorII}[1]{  \ensuremath{ \ushortd{{\boldsymbol{#1}} } } }
+\newcommand{\tensorIII}[1]{ \ensuremath{ \underaccent{3}{ \underaccent{\tilde}{ {\boldsymbol{#1}} } } } }
+\newcommand{\tensorIV}[1]{  \ensuremath{ \underaccent{4}{ \underaccent{\tilde}{ {\boldsymbol{#1}} } } } }
+% bm variant
+%\usepackage{bm}   % load bm after amsmath and after your font packages!; for tensor
+%\newcommand{\tensorI}[1]{   \ensuremath{ \uline{  \bm{#1} } } }
+%\newcommand{\tensorII}[1]{  \ensuremath{ \uuline{ \bm{#1} } } }
+%\newcommand{\tensorIII}[1]{ \ensuremath{ \underaccent{3}{ \underaccent{\tilde}{ \bm{#1} } } } }
+%\newcommand{\tensorIV}[1]{  \ensuremath{ \underaccent{4}{ \underaccent{\tilde}{ \bm{#1} } } } }
 
 %needs MnSymbol
 \newcommand{\tensori}[1]{
@@ -356,23 +416,46 @@
 \usepackage{amsthm}
 \theoremstyle{definition}
 % nummeriert
+\newtheorem{tDef}{Def}
 \newtheorem{tBsp}{Bsp}
 % unnummeriert
-\newtheorem*{tDef}{Def}
+\newtheorem*{tDef*}{Def}
 \newtheorem*{tBsp*}{Bsp}
 
 \newcommand{\undertab}[1]{\clap{%
   \scriptsize\begin{tabular}{@{}c@{}}#1\end{tabular}}}
+% underbrace, centered, space corrected
 \newcommand{\ubspace}[2]{% Correct \underbrace spacing
-  \mathrlap{\underbrace{\phantom{#1\strut}}_{\undertab{#2}}}#1}
+  \mathrlap{\underbrace{\phantom{\scalebox{0.95}{$#1$}\strut}}_{\undertab{#2}}}#1}
+% underbrace, left aligned, space corrected
 \newcommand{\ubspacel}[2]{% Correct \underbrace spacing
+  \mathrlap{\underbracket[0pt][0pt]{\phantom{\scalebox{0.95}{$#1$}\strut}}_{\vphantom{\big\mid}\text{#2}}}\underbrace{#1}}
+% underbrace line, left aligned, space corrected
+\newcommand{\ubspacell}[2]{
   \mathrlap{\underbracket[0pt][0pt]{\phantom{#1\strut}}_{\text{#2}}}\underbracket[0.5pt][0pt]{#1}}
 
 %\usepackage{eurosym}	% fuer das Eurosymbol
 %\DeclareUnicodeCharacter{20AC}{\euro{}}
 
+\usepackage{cancel}
 
 
+%\begin{pmatrix}[1.5]  -> \arraystretch{1.5}
+\makeatletter
+\renewcommand*\env@matrix[1][\arraystretch]{%
+  \edef\arraystretch{0.8}%
+  \edef\arraystretch{#1}%
+  \edef\arraycolsep{2pt}%
+  \hskip -\arraycolsep
+  \let\@ifnextchar\new@ifnextchar
+  \array{*\c@MaxMatrixCols c}}
+\makeatother
+
+\newenvironment{Array}[1]{
+  \begingroup
+  \arraycolsep=1pt\def\arraystretch{1}
+  \begin{array}{@{}#1@{}}
+}{\end{array}\endgroup}
 
 
 % -----------------------------------------
@@ -535,6 +618,11 @@
 
 % !!!! in tikzset sind keine Leerzeilen erlaubt !!!!
 \tikzset{
+    %scale a tikzpicture including texts
+    global scale/.style={
+           scale=#1,
+           every node/.style={scale=#1}
+    },
     %Define standard arrow tip
     >=stealth',
     %Define standard node
@@ -735,3 +823,13 @@
 \makeatletter
 \def\mynobreakpar{\par\nobreak\@afterheading}
 \def\mynobreakline{\par\nobreak\vspace{-\parskip}\@afterheading\noindent} \makeatother
+
+
+\newenvironment{absolutelynopagebreak}
+  {\par\nobreak\vfil\penalty0\vfilneg
+   \vtop\bgroup}
+  {\par\xdef\tpd{\the\prevdepth}\egroup
+   \prevdepth=\tpd}
+%\begin{absolutelynopagebreak}
+%\lipsum[1-3]\lipsum*[4]
+%\end{absolutelynopagebreak}